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Vortex Pinning and Sliding in Superconductors
Charles Simon, laboratoire CRISMAT, CNRS
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Laboratoire CRISMATA. PautratC. Goupil
Ecole Normale Supérieure ParisP. Mathieu
LEMA ToursA. RuyterL. Ammor
Laboratoire Léon BrillouinA. Brûlet
Institut Laue LangevinC. Dewhurst
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I Introduction to vortex pinning and dynamics
II A neutron diffraction study in low Tc materials
III The peak effect in NbSe2
IV The surface pinning in Bi-2212V Conclusions
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Vortex dynamics
V
BFLI Vff
0 5 10 15 200
1
2
3
I (A)
V (
mV
)0.1 T
0.2 T
0.3 T
I c (B)
Nb-Ta
4.2 K
V= Rff(B,T) (I-Ic(B,T))
E=B. Vff
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Typical disordered elastic system with pinning and sliding with the possibility to vary the intensity of the pinning by changing the magnetic field.
But from the beginning: problems (shape of the IV, …)
Here : Low temperature physics Neutron scattering, very difficult but quite
simple to interpret (10 years)
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Neutron scattering
B
T
Bc2
Bc1Meissner
Normal phase
Niobium
Nb-Ta
Bi-2212
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B(G)
Cubitt, R. et al. Nature 365, 407-411 (1993).
T. Giamarchi and P. Le Doussal, Phys. Rev. Lett. 72, 1530 (1994).and Phys. Rev. B 52, 1242 (1995).
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T. Klein et al., Nature 413, (2001) 404
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Neutrons with current
Nb-Ta singlecrystal
P. Thorel and al., J. Phys. (Paris) 34, 447 (1973).A. Pautrat, Phys. Rev. Lett. 90, 087002 (2003).
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Neutrons with current
Nb-Ta singlecrystal
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How flows the current?
Ic/2Ibulk=0
Ic/2 Ic/2
Ic/2Ibulk=(I-Ic)
Bneutrons
curl B = J
tan by / B = Jxe / B
A. Pautrat, et al. Phys. Rev. Lett. 90, 087002 (2003)
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surface pinning (Pb-In)
0
0.2
0.4
0.6
0.8
1
1.2
0 2 4 6 8
V(I)
C
V(m
V)
I (A)
Ic
0 0.1 0.2 0.3 0.4 0.50
10
20
30
40
B (T)
I c (A
)
Bc2 (4.2 K)
Ic (
Am
p)
Surface treatments
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Why surface pinning?
Normal rough surface
ic (A/m) = . sin cr
B
1000 Å
MS length
P. Mathieu et Y. Simon, Europhys Lett 5, 1988
~ 0-100 A/cm
ic v (o/B)1/2 ao
Boundary conditionsncr
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 0.2 0.4 0.6 0.8 1
/ H
C2
/ BC2
= 1
Numerical solution of Ginzburg equationsby Guilpin and Simon
Nb film
deg10.070.0 cr
Quantitative prediction
Quantitative analysis of the critical current due to vortex pinning by surface corrugation A. Pautrat, J. Scola, C. Goupil, Ch. Simon, C. Villard, B. Domengès, Y. Simon,
B. Phys. Rev. B 69, 224504 (2004)
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What happens at high current?
0
1
2
3
4
5
6
0 5 10 15 20 25 30
B
V=Rff (I-Ic)V(m
V)
I(A)
0
0.2
0.4
0.6
0.8
0 2 4 6 8 10 12 14 16
Ic
(
deg
)
I (Amp)
0
100
200
300
400
500
600
0 1 2 3 4 5 6
V (V
)
0
50
100
150
200
250
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
0 5 10 15 20
Ic
Smooth surface Rough surface
(d
eg)
I (Amp)
V (V
)
0
0.02
0.04
0.06
0.08
0.1
0.12
-0.5 0 0.5 1 1.5
(deg)
0 A
20 A
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Inhomogeneous critical current
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20
Ic min
< Ic >
0
500
1000
1500
2000
0 5 10 15 20
(
deg
)V
(V
)
Ic1 < I < Ic2
Ic1Ic2 Ic2
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The peak effect in NbSe2
0 1 2 3 4 5 6
0
20
40
60
FCZFC
2K 0.4TV
(V)
I(Amps)
0 2 4 6 8 100
200
400
0.3T
1T
1.5T
V(V
)
I(Amps)
Metastable states of a flux-line lattice studied by transport and small-angle neutronA. Pautrat, J. Scola, Ch. Simon, P. Mathieu, A. Brûlet, C. Goupil, M. J. Higgins,
Phys. Rev. B 71, 064517 (2005)
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0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60
50
100
150
200
250
Bc2
(c)=B
c2(0)/(cos2+-2sin2)1/2
tan=2tan =3
Jc=sinc B
c (1-B/B
c2)/21/2
c=9°
c=0.9°
4.2KNbSe
2
Jc(A
/cm
)
B(T)
NbSe2
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Iron doped NbSe2
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0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.60
50
100
150
200
250
Bc2
(c)=B
c2(0)/(cos2+-2sin2)1/2
tan=2tan =3
Jc=sinc B
c (1-B/B
c2)/21/2
c=9°
c=0.9°
4.2KNbSe
2
Jc(A
/cm
)
B(T)
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T. Klein et al., Nature 413, (2001) 404
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Bi-2212 Transport in the peak effect
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Bi-2212
Persistence of an ordered flux line lattice above the second peak in Bi2Sr2CaCu2O8+δ A. Pautrat, Ch. Simon, C. Goupil, P. Mathieu, A. Brûlet, C. D. Dewhurst, and A. I. Rykov
Phys. Rev. B 75, 224512 (2007)
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Bi-2212 with columnar defects
5K 0.4T
B=1T
Microbridge 50m20 m
Surface vortex depinning in an irradiated single crystal microbridge of Bi2Sr2CaCu2O8+δ : Crossover from individual to collective bulk pinning
A. Ruyter, D. Plessis, Ch. Simon, A. Wahl, and L. Ammor Phys. Rev. B 77, 212507 (2008)
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Do columnar defects product bulk
pinning?
No, there is no bulk currents
Do Columnar Defects Produce Bulk Pinning ? M. V. Indenbom, C. J. van der Beek, M. Konczykowski, and F. Holtzberg Phys. Rev. Lett. 84, 1792 (2000)
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Reversible magnetization
A. Wahl et al., Physica C 250 163(1995)
R. J. Drost et al, PRB 58 R615 (1998)
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Very powerful technique
Surface currents Peak effect = metastable states
What is the limit of this stability? Noise measurements, ac response, Hall
effects…
Conclusions